相关论文: Derivations on triangular Banach algebras of order…

In this paper, we study several type of point derivations for Banach algebras. We investigate how our definition of point derivations are related to each others.

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

In the paper I considered definition and structure of linear mapping of Banach algebra over commutative ring. Based on this definition I explore derivative of continuous mapping.

We introduce a class of Banach algebras of generalized matrices and study the existence of approximate units, ideal structure, and derivations of them.

In this paper, we define $\omega$-derivations, and study some properties of $\omega$-derivations, with its properties we can structure a new $n$-ary Hom-Nambu algebra from an $n$-ary Hom-Nambu algebra. In addition, we also give derivations…

In this paper we investigate in details derivations on trivial extension algebras. We obtain generalizations of both known results on derivations on triangular matrix algebras and a known result on first cohomology group of trivial…

In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…

Our constructions provide a systematic way to study cohomology tri-dendriform algebra via classical cohomology, simplifying computations and enabling the use of established techniques.

We study the concept of extended derivations of algebras which expands diverse definitions of generalized derivations given in the literature. We concentrate on the family of the anti-commutative algebras and classify such spaces of…

In this article we shall focus on the derivations on module extension of Banach algebras and determine the general structure of them. Then we obtain some results concerning the automatic continuity of these mappings.

We give a brief overview of the area of Banach algebras, intended for a general mathematical audience.

Let ${\mathcal N}$ be the Lie algebra of all $n\times n$ strictly block upper triangular matrices over a field ${\mathbb F}$ relative to a given partition. In this paper, we give an explicit description of all derivations of ${\mathcal N}$.

Triangular algebras, and maximal triangular algebras in particular, have been objects of interest for over fifty years. Rich families of examples have been studied in the context of many w$^*$- and C$^*$-algebras, but there remains a dearth…

The concepts of derivations and right derivations for Leibniz algebras and $K$-B quasi-Jordan algebras naturally arise from the inner derivations determined by their algebraic structures. In this paper we introduce the corresponding…

We explicitly describe the Lie algebras $M_L$ of ladder matrices in $M_n$ associate with dominant upper triangular ladders $L$, and completely characterize the derivations of these $M_L$ over a field $F$ with $char(F) \neq 2$. We also…

In recent work of the authors the notion of a derivation being approximately semi-inner arose as a tool for investigating (approximate) amenability questions for Banach algebras. Here we investigate this property in its own right, together…

In terms of triples of Banach spaces, we define a large class of boundary problems for ordinary differential equations (of arbitrary order) with singular coefficients.

All complex $3$-dimensional nilalgebras were described. As a corollary, all degenerations in the variety of complex $3$-dimensional nilalgebras were obtained.

In the book, I considered differential equations of order $1$ over Banach $D$\Hyph algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. I considered examples of…

This article gives a summary of the finite-dimesional irreducible representations of the $q$-Onsager algebra, which are treated in detail in our paper `The augmented tridiagonal algebra'.